Affine Grassmannian slices and their quantizations

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

Slices in the affine Grassmannian are geometric incarnations of weight spaces of representations of semisimple complex groups. These spaces can also be constructed as Coulomb branches of quiver gauge theories or in type A, as bow varieties. They are related to Nakajima quiver varieties using 3d mirror symmetry, also known as symplectic duality. These spaces are conical symplectic singularities and have natural quantizations using algebras called truncated shifted Yangians. I will survey 10 years of research on these wonderful spaces and describe some remaining open questions.